Focusing and Saturation of the internal tide

Abstract

The interaction of tidal currents with sea-floor topography generates internal gravity waves, called internal tides. Their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in mixing the abyssal ocean and hence in controlling the large-scale ocean circulation. As part of on-going work to understand the vertical distribution of wave breaking over sea-floor topography, we investigate the instability of internal tides in a simple linear model. For two-dimensional tides over one-dimensional topography, the formation of unstable regions is closely linked to singularities in the topography shape. For three-dimensional tides over two-dimensional topography there is in addition a geometric focusing of wave energy into localized regions of high wave amplitude, which we investigate through simple examples. Overall, the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.